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4 Introduction to Carbon Materials 2s 1s ground state excited state ( ~ 4 eV) ~ 4 eV xyz xyz 2s 1s 2p 2p 2p 2p 2p 2p Figure 1.2: Electronic configurations for carbon in the ground state (left) and in the excited state (right). put 2 electrons in the 2s orbital and only 2 of them in the 2p orbitals (Fig 1.2). It turns out, however, that in the presence of other atoms, such as e.g. H, O, or other C atoms, it is favourable to excite one electron from the 2s to the third 2p orbital, in order to form covalent bonds with the other atoms. The gain in energy from the covalent bond is indeed larger than the 4 eV invested in the electronic excitation. In the excited state, we therefore have four equivalent quantum-mechanical states, |2s⟩, |2px⟩, |2py⟩, and |2pz⟩. A quantum-mechanical superposition of the state |2s⟩ with n |2pj⟩ states is called spn hybridisation, which play an essential role in covalent carbon bonds. 1.1.1 sp1 hybridisation In the sp1 hybridisation,3 the |2s⟩ state mixes with one of the 2p orbitals. For illustration, we we have chosen the |2px⟩ state. A state with equal weight from both original states, is obtained by the symmetric and anti-symmetric combinations 11 |sp+⟩ = √2 (|2s⟩ + |2px⟩) , |sp−⟩ = √2 (|2s⟩ − |2px⟩) . The other states, |2py⟩ and |2pz⟩, remain unaffected by this superposition. The electronic density of the hybridised orbitals has the form of a club and 3The superscript is often omitted, and one may alternatively use “sp hybridisation”. EnergyPDF Image | Physical Properties of Graphene
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